Anomalous Resonance of the Symmetric Single-Impurity Anderson Model in the Presence of Pairing Fluctuations

TL;DR

This paper investigates the symmetric single-impurity Anderson model with pairing fluctuations, revealing an anomalous resonance at the Fermi level with exact self-energy derivation and renormalization effects.

Contribution

It provides an exact analysis of the hybridizing and non-hybridizing modes, uncovering a singular resonance in the non-hybridizing modes due to pairing fluctuations.

Findings

Exact self-energy for hybridizing modes shows two subbands at ±U/2.

Non-hybridizing modes exhibit a marginal Fermi liquid resonance.

Resonance is pinned at the Fermi level but weakened by renormalization.

Abstract

We consider the symmetric single-impurity Anderson model in the presence of pairing fluctuations. In the isotropic limit, the degrees of freedom of the local impurity are separated into hybridizing and non-hybridizing modes. The self-energy for the hybridizing modes can be obtained exactly, leading to two subbands centered at $\pm U/2$. For the non-hybridizing modes, the second order perturbation yields a singular resonance of the marginal Fermi liquid form. By multiplicative renomalization, the self-energy is derived exactly, showing the resonance is pinned at the Fermi level, while its strength is weakened by renormalization.